Apparatus for well logging measuring and comparing potentials caused by sonic excitation

ABSTRACT

A sonic transducer in contact with the surface of a formation traversed by a bore hole periodically excites the formation at low frequencies to cause periodic flow of the formation fluid and therefore periodic electrokinetic potentials to be created in the formation. The potentials are measured at a location near the transducer and at least at one other location spaced from the transducer, and the ratio of the measured potentials provides knowledge of the electrokinetic skin depth of the formation and thus of the relative and actual permeability of the formation.

United totes Patent [72] Inventor Adelbert Semmelink Chicago, 111. [21]Appl. No 832,679 [22] Filed June 12, 1969 [45] Patented Aug. 10, 1971[73] Assignee Schlumberger Technology Corporation Houston, Tex.

[54] APPARATUS FOR WELL LOGGING MEASURING AND COMPARING POTENTIALSCAUSED BY SONIC EXCITATION 9 Claims, 3 Drawing Figs.

[52] US. Cl 324/1,

324/10 [51] 1nt.Cl G01v3/18 [50] Field of Search 324/1, 10

[56] References Cited UNITED STATES PATENTS 2,433,746 12/1947 Doll 324/12,814,017 11/1957 Doll 324/1 2,965,838 12/1960 *324/1 2,974,273 3/1961324/1 3,002,148 9/1961 324/1 3,075,142 l/l963 324/1 3,116,449 12/1963324/10 X 3,268,801 8/1966 Clements et a1. 324/10 Primary ExaminerGerardR. Strecker Attorney-Brumbaugh, Graves, Donohue & Raymond econnen METERPHASE PATENTEU AUG 1 01971 RECORDER FIG 3 INVEN'IOR.

ADELBERT SEMMELINK his A T TORNEYS APPARATUS FOR WELL LOGGING MEASURINGAND COMPARING POTENTIALS CAUSED BY SONIC EXCITATION BACKGROUND OF THEINVENTION The present invention relates to methods and apparatus forinvestigating the permeability of earth formations traversed by a borehole, and more particularly to novel and improved methods and apparatusfor determining the relative or actual permeabilities of the formationsby obtaining indications of the rate of fall-off in fluid velocity in aformation, and of the electrokinetic skin depth of fluid flow in aformation, by applying low-frequency sonic energy to the formationsurface and measuring the resulting electrokinetic potentials generatedin the formation at selected locations.

l-leretofore, information relating to the location and permeability ofsubsurface earth formations has been obtained by electrical loggingmethods which are based at least in part on the electrokinetic potentialphenomenon that occurs when relative movement is induced between aformation and the fluid contained in the matrices of the formationmaterial. For example, in the US. Pat. No. 2,814,017, issued Nov. 19,1957 to Henri-Georges Doll and assigned to the assignee of thisinvention, methods are described for investigating the permeabilities ofearth formations by observing the differences in phase between periodicpressure waves passed through the formations and the potentialsgenerated by the oscillatory motion of the formation fluid caused bythese pressure waves. Conversely, a periodically varying electriccurrent can be used to generate oscillatory motion of the formationfluid, which in turn generates periodic pressure waves in the formation.Measurements can be readily made of the phase displacement between thegenerating and the generated quantities and a direct indication of therelative permeability of the formation thereby obtained.

Although these methods yield useful data relating to the permeability ofsubsurface formations and, accordingly, have been a significantcontribution to the art, it is desirable to obtain permeabilityinformation through other methods and, more particularly, through themeasurement of the magnitudes of electrokinetic potentials generated ina formation by low-frequency sonic excitation of the formation surface.By using low-excitation frequency methods, significant advantages arerealized, including eliminating the need of a bore hole pressure probeand minimizing the effects of mud filter cakes on electrical loggingtechniques.

It has been discovered that the application of low-frequency sonicenergy to a formation surface creates large electrokinetic, orstreaming, pulses in the immediate area of the sonic generator. Thisvoltage distribution may be visualized as being caused by periodicradially directed surges of fluid in the formation resulting from thelocalized periodic compression, or squeezing," of the formation surfaceat the area of contact with the sonic generator. The flow in questionmay be considered to be similar to an alternating double layer of smallradial extent having a thickness of the order of the electrokinetic skindepth of fluid flow in the formation. Electrokinetic skin depth,moreover, is defined as the distance in which the relative motion offlow in the outward sense diminishes by a factor of He, where e is thenatural logarithm base, a value of approximately 2.72.

In any event, the streaming potential pulses generate periodic movementsof the formation fluid which produce detectable transient electrokineticpotentials of the same frequency as the applied sonic energy and havingmagnitudes at any given location directly proportional to the velocityof the fluid motion at that location and inversely proportional to thesquare of the distance from the locus of the streaming potential pulse.Since the fluid velocity necessarily falls off from its initial valuewith increasing length of travel through the formation at a ratedependent in part upon the permeability of the formation rock, it will'be appreciated that the magnitude of the electrokinetic potential atany given distance from the streaming pulse will be an indication offormation permeability. Thus, a high-electrokinetic skin depth would beindicative of a large relative movement between the formation and theformation fluid and a high permeability, while a lowelectrokinetic skindepth at the same location would indicate that the formation isconstituted of relatively impermeable material.

By obtaining measurements, while the formation is excited, of themagnitudes of the electrokinetic potentials existing at one or morefixed locations spaced from the sonic generator, and thus from thestreaming potential pulses, and referencing them to the magnitude of thestreaming pulses, it is possible to obtain data indicative of the rateof fall-off in fluid velocity. These data may be compared with similardata from formations of known permeability, such as formations whichhave been investigated by core analysis, for example, to make aqualitative determination of the relative permeability of the formationbeing investigated.

It is also possible to determine actual permeabilities, and tofacilitate the development of relative permeability data, by relatingthe fluid velocity fall-off measurements to the electrokinetic skindepth of fluid flow in the formation. Although the exact nature of thephysical relationship between the measured quantities and the skin depthis not known, specific values can be measured experimentally. Forexample, onediminsional laboratory tests indicate that the measuredpotential falls off as a function of e, where z is the distance betweenthe point of measurement and the sonic generator, and 6 is theelectrokinetic skin depth. Other studies that more closely approximatebore hole conditions, however, seem to show that the potential decreasesin accordance with an inverse power law series. In any case,notwithstanding the physical character of the phenomenon, the ratio ofthe electrokinetic potential magnitudes at spaced locations from thesonic generator to the magnitude of the streaming pulse is known to berelated to the skin depth in a manner which can be determinedexperimentally.

Turning once more to the linear flow situation, the average flow rate ofthe fluid in the formation can be expressed as follows, through asolution of the well known diffusion equation:

where q is the average flow rate of the fluid at a depth 2 from theformation surface 6 is the average flow rate of the fluid at theformation surface, i.e., z=o z is the depth from the formation surface 8is the electrokinetic skin depth m is the product of 211' and the sonicfrequency.

The electrokinetic skin depth can then be expressed as:

where 6 is the skin depth 0 is sound velocity in the (bulk) fluid k isthe formation permeability p is the fluid density p. is the viscosity ofthe formation fluid w is the product of 211' and the sonic frequency isthe formation porosity.

Expressing the potential ratios in terms of the skin depth isparticularly useful, therefore, in that it allows calculation, bysolution of the above equation, of the actual permeability of theformation tested. Obviously, the viscosity and density of the formationfluid, the sound velocity in the formation fluid and the porosity of theformation material must be known in order to determine the actualpermeability. This information can be obtained through conventionaltechniques.

SUMMARY OF THE INVENTION There are provided, in accordance with theinvention, methods and apparatus for determining the actual or relativepermeability of subsurface earth formations, including the steps ofapplying sonic energy to the surface of a formation to cause periodicmotion of the formation fluid, and thereby periodic electrokineticpotentials, to be created in the formation, and measuring the magnitudesof the electrokinetic potentials near the location where the sonicenergy is applied and at least at one other location in nearby spacedrelation to the sonic generator to obtain indications of the rate offall-off in fluid velocity and of the electrokinetic skin depth of fluidflow in the formation. Preferably the sonic generator is positioned at anumber of depths along any given formation and the formation is excitedat each depth at a plurality of separate frequencies. By comparing theindications thus obtained with similar indications from earth formationsof known permeability, the relative permeability of the formationsinvestigated can be determined.

More specifically, a method of investigating earth formations accordingto the present invention includes positioning a sonic transducer incontact with the surface of a formation to be investigated and applyingsonic energy to the formation at frequencies within the range of from to500 c.p.s. to cause periodic fluid flow and thereby periodicelectrokinetic potentials to be created in the formation. Thesepotentials are detected by an electrode system, which includes a centerelectrode positioned closely adjacent the transducer, a ground electrodeand at least one outer electrode disposed at a location spaced from thetransducer, and their respective magnitudes recorded by suitableinstrumentation at the earths surface. The outer electrode may, forexample, be located within three electrokinetic skin depths of thetransducer.

The ratio of the electrokinetic potential at each spaced electrode tothe magnitude of the potential at the center electrode is thendetermined for each excitation frequency to obtain an indication of therate of fall-off in fluid velocity between the source of excitationenergy and the location of the spaced electrodes, which indications arethen compared with the falloff rates of formations of known permeabilityto make qualitative determinations of the relative permeability of theformation tested.

Since the ratios of the electrokinetic potential magnitudes at thespaced electrodes and the transducer electrode can be relatedexperimentally to the electrokinetic skin depth of the formation, it ispossible to calculate the actual permeability of the formation if theviscosity, density and sound velocity of the formation fluid are knownand the porosity of the formation material is known. If the viscosity isnot known, the specific permeability, i.e.,"/ ,u., can be derived. Inmany instances, specific permeability may be a more useful loggingparameter than permeability.

Also, the measured quantities can be indicated and recorded directly asskin depth values to facilitate comparison with the skin depth values ofpreviously investigated formations and to put the data in a form fromwhich actual permeabilities can readily be determined.

BRIEF DESCRIPTION OF THE DRAWINGS For a better understanding of theinvention, reference may be made to the following detailed descriptionof a representative embodiment, taken in conjunction with the figures ofthe accompanying drawings in which:

FIG. 1 is a schematic diagram of suitable apparatus for investigatingthe permeability of earth formations traversed by a borehole inaccordance with the present invention; and

FIG. 2 is a top view of the apparatus, taken along the line 2-2 of FIG.1 and looking in the direction of the arrows; and

FIG. 3 is a detail elevation view of the logging device of theapparatus, taken along the line 3-3 of FIG. 1 and looking in thedirection of the arrows.

DESCRIPTION OF A REPRESENTATIVE EMBODIMENT Referring particularly toFIG. 1, representative apparatus for investigating the permeability ofsubsurface earth formations in accordance with the invention is showndisposed in an uncased bore hole 10 traversing a subsurface earthformation 12 and containing a bore hole fluid 14. The bore holeapparatus may include a sonic well tool 16 supported by a cable 18 andmay be raised and lowered in the bore hole by conventional winch means(not shown) located at ground level.

The sonic well too] 16 comprises an elongated housing 20 having alogging device 22 for engaging the surface of the formation 12 andmeans, such as the diametrically disposed, wallengaging bow spring 24,for resiliently urging the housing 20 and the logging device 22 towardthe opposite bore hole wall to hold the logging device 22 in firmengagement with the surface of the formation.

The logging device 22 (FIG. 2) preferably conforms generally to thecontour of the bore hole wall and is supported on the housing 20 byextensible members 26 so as to be selectably movable between anoutboard, wall-engaging position and an inboard, retracted position. Inthe illustrative embodiment shown, the logging device is maintained atthe inboard position during movement of the tool 16 in the borehole andis caused to be extended from the housing into engagement with aformation to be tested by activation of a hydraulic system, for example,from the ground surface.

Sonic generating means 29 (FIG. 3), such as an hydraulic transducer, ismounted on the outer face of the logging device 22 and is adapted to bebrought into contact with the adjacent surface of the formation. Thegenerating means 28 may be energized by a suitable source of electricalenergy 30 (FIG. 1) located at the ground surface and connected to thegenerator through a conductor 32 carried by the cable 18. Electrokineticpotentials resulting from the fluid flow created in the formation by theapplied sonic energy are detected by a system of electrodes mounted onthe logging device 22 and including a center electrode 34, a commonelectrode 36 and at least one outer electrode 38 spaced from the centerelectrode. The electrodes 34 and 38 are connected through conductors 40,44, respectively, in the cable 18 to suitable indicating and recordingapparatus 46 at the surface of the earth. A phase meter 48 may beinterposed between the apparatus 46 and the electrodes for a purposehereinafter described.

The center electrode 34 is mounted close enough to the transducer 28 todetect the large streaming potential pulses created by the periodiccompression of the formation surface by the applied sonic energy. On theother hand, the outer electrode 38 is spaced sufficiently distant fromthe transducer 21 so that it detects only the electrokinetic potentialscaused l the motion of the formation fluid. To this end, the spacingbetween the outer electrode 38 and the transducer 28 should be large incomparison with the electrokinetic skin depth of fluid flow in theformation. Since the skin depths of commercially valuable formations arequite small, a typical value being several centimeters, the desiredelectrode spacing can easily be achieved on presently available welltools.

In operation, the well tool 16 is positioned opposite a formation to beinvestigated, the logging device 22 is extended into engagement with theformation surface and the transducer 28 is activated to excite theformation. In accordance with the invention, the frequency of excitationis low and typically within the range of from 20 to 500 c.p.s.Thereafter, and while the formation is being excited, the magnitudes ofthe streaming potential pulses and the resultant electrokineticpotentials are detected by the center electrode 34 and the outerelectrode 38, respectively, referenced to an arbitrary point through theelectrode 36 and recorded by the indicating and recording apparatus 46.So that reliable indications of the several potentials are obtained,measurements should be made continuously over a 4 to S-cycle period ofexcitation. Moreover, as the electrokinetic skin depths are dependentupon the frequency of the applied sonic energy, measurements of thepotentials are preferably made at a plurality of separate frequencies ateach depth in the bore hole at which a formation is tested. In addition,the permeability at one depth can be determined relative to that atanother depth through an observation of the frequency ratio at the twobore hole depths within the bore hole necessary to achieve the same skindepth.

Turning again to measurements at one bore hole depth, the ratios of themagnitude of the potentials at the outer electrode 38 to that of thestreaming pulses at the electrode 34 are then determined to obtainindications of the rate of fall-off in fluid velocity in the formation.Although the potential ratios can be calculated manually, theypreferably are determined by suitable automatic calculating apparatus,as by an analog or digital computer, for example, which conveniently canbe operatively connected to the indicating and recording apparatus 46.The data thus generated are then compared with similar data fromformations of known permeability to obtain qualitative determinations ofthe relative permeability of the formation investigated.

It will be understood, of course, that any desired number of outerelectrodes can be provided at spaced intervals along the surface of thelogging device 22 and the data thereby provided conveniently compiled,for example, as a plot of the electrokinetic potentials measured at eachelectrode, and referenced to an arbitrary ground, against the distancefrom the center electrode. Such a presentation of the data greatlyfacilitates relative permeability studies.

Alternatively, the fluid flow rate data obtained by measuring theelectrokinetic potentials can be indicated and recorded in terms of theelectrokinetic skin depth of the formation, and suitable calculatingapparatus can be operatively connected to the indicating and recordingapparatus for this purpose. A significant advantage of developing thedata in this form is that it makes possible the determination of theactual permeability of a formation, through a solution of theaforementioned skin depth equation, either manually or automatically,whenever the viscosity, density and sound velocity of the formationfluid and the porosity of the formation material are known. On the otherhand, it also facilitates the development of relative permeability data,such as, for example, relative permeability logs of the formationstraversed by a bore hole, by allowing ready comparison of the data withreference data from previously investigated formations.

If desired, measurements can be made through the use of a phase meter 48of the phase of the generated electrokinetic potentials or of the phasedisplacement between the applied periodic sonic energy and the periodicelectrokinetic potentials at the outer electrodes to provide furtherinformation concerning the permeability of the formation material and tofacilitate the determination of electrokinetic skin depth values.Alternatively, the phase meter 48 can be coupled to the generator toprovide a phase reference. A doublethrow, single-pole switch may be usedto connect the phase meter 48 selectively to either the conductor or theconductor 44, depending on which electrode is under observation.

The presence of mud cake on the bore hole walls, as is typical of rotarydrilled wells, does not have a material effect on the results obtainedby the methods of the present invention since the low-frequency sonicenergy is still effective to compress the formation surface and therebycause the periodic electrokinetic potentials to be created in theformation. Moreover, the mud cakes are typically very much lesspermeable than earth formations of commercial interest and, therefore,the electrokinetic skin depths associated with the movement of the mudfiltrate through the cake are very small in comparison to theelectrokinetic skin depths associated with the formation beinginvestigated. In consequence, the major components of the streamingpotential pulses measured at the center electrode and of theelectrokinetic potentials measured at the outer electrodes areattributable to the movement of the formation fluid through theformation material. Again, indications of relative permeability can beobtained by comparing the ratios of the measured potentials or phasedisplacements to similar values obtained from formations of knownpermeability that are also traversed by a mudded-off bore hole.

It will be understood by those skilled in the art that theabove-described embodiment of the invention is intended to be merelyexemplary, and that it is susceptible of modification and variationwithout departing from the spirit and scope of the invention. Forexample, other means may be employed for applying sonic energy to aformation surface, such as, for example, an electroacoustical transducerapparatus of the type disclosed in the prior art U.S. Pat. No.3,138,219. All such variations and modifications, therefore, areincluded within the scope of the invention as set forth in the appendedclaims.

I claim:

1. A method for investigating the permeability of earth formationstraversed by a bore hole and containing a fluid in the pores thereofcomprising:

positioning a source of periodic mechanical excitation in contact withthe surface of the bore hole within a formation to be investigated,

actuating the source to periodically excite the formation at the area ofcontact between the formation and the excitation source so as to causeperiodic electrokinetic potentials of relatively large magnitude to beproduced at the contact area and separate, periodic electrokineticpotentials of proportionally smaller magnitude to be produced atlocations spaced from the contact area,

simultaneously with excitation of the formation measuring the magnitudeof the relatively large electrokinetic potentials at the contact areaand the magnitude of the proportionally smaller electrokineticpotentials at at least one other location spaced from the contact by adistance large relative to the electrokinetic skin depth of theformation, and

determining the ratio of the magnitude of the electrokinetic potentialsat each other location to the magnitude of the electrokinetic potentialsat the contact area, said ratio being an indication of the permeabilityof the formation.

2. A method according to claim 1 further comprising:

sequentially exciting the formation at a plurality of separatefrequencies,

measuring the magnitude of the relatively large electrokineticpotentials at the contact area and the magnitude of the proportionallysmaller electrokinetic potentials at at least one other location spacedfrom the contact area by a distance large relative to the electrokineticskin depth of the formation at each separate frequency of excitation,and

determining the ratio of the magnitude of the electrokinetic potentialsat each other locations to the magnitude of tht electrokineticpotentials at the contact area at each separate frequency. 3. A methodaccording to claim 2 in which the frequencies at which the formation isexcited are within the range of from 20 to 500 c.p.s.

4. A method for investigating the permeability of earth formationstraversed by a bore hole and containing a fluid in the pores thereofcomprising:

positioning a sonic transducer in contact with the surface of the borehole within a formation to be investigated,

actuating the transducer to periodically excite the formation at thearea of contact between the transducer and the formation so as to causeperiodic electrokinetic potentials of relatively large magnitude to beproduced at the contact area and separate, periodic electrokineticpotentials of proportionally smaller magnitude to be produced at 10-cations spaced from the contact area,

simultaneously with excitation of the formation measuring the magnitudeof the relatively large electrokinetic potentials at the contact areaand the magnitude of the proportionally smaller electrokineticpotentials at at least one other location spaced from the contact areaby a distance large relative to the electrokinetic skin depth of theformation, and

determining the ratio of the magnitude of the electrokinetic potentialsat each other location to the magnitude of the electrokinetic potentialsat the contact area, said ratio being an indication of the permeabilityof the formation.

5. A method according to claim 4 further comprising:

sequentially exciting the formation at a plurality of separatefrequencies,

measuring the magnitude of the relatively large electrokineticpotentials at the contact area and the magnitude of the proportionallysmaller electrokinetic potentials at at least one other location spacedfrom the contact area by a distance large relative to the electrokineticskin depth of the formation at each separate frequency of excitation,and

determining the ratio of the magnitude of the electrokinetic potentialsat each other location to the magnitude of the electrokinetic potentialsat the contact area at each separate frequency.

6. A method according to claim 5 in which the frequency at which theformation is excited is within the range of from to 500 c.p.s.

7. Apparatus for investigating the permeability of earth formationstraversed by a bore hole and containing a fluid in the pores thereofcomprising:

a source of periodic mechanical excitation, means for positioning theexcitation source in contact with the bore hole wall with a formation tobe investigated, means for actuating the source to periodically excitethe formation at the area of contact between the source and the borehole wall so as to cause periodic electrokinetic potentials ofrelatively large magnitude to be produced at the contact area andseparate, periodic electrokinetic potentials of a proportionally smallermagnitude to be produced at locations spaced from the contact area,means for measuring the magnitude of the relatively large electrokineticpotentials at the contact area and the magnitude of the proportionallysmaller electrokinetic potentials at at least one other location spacedfrom the contact area by a distance large relative to the electrokineticskin depth of the formation during excitation of the formation,

and means for determining the ratio of the magnitude of theproportionally smaller electrokinetic potentials at each other locationto the magnitude of the relatively large electrokinetic potentials atthe contact area, said ratio being an indication of the permeability ofthe formation. 8. Apparatus according to claim 7 in which the source ofperiodic mechanical excitation comprises a sonic transducer.

9. Apparatus according to claim 8, in which the sonic transducer isadapted to produce excitation frequencies within the range of from 20500 c.p.s.

mg? UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No.3,599,085 Dated August 10, 1971 Inventor(s) Adelbert Semmelink It iscertified that error appears in the above-identified patent and thatsaid Letters Patent are hereby corrected as shown below:

' IN THE TITLE, line 1, after "LOGGING" insert -BY-; Col. 2,

line 45, "=oe /6 cos (m+z/6" should be 1 8 T cos (w+)-;

Col. 2, line 58, "6=\/2kp/w11 should be --a c1fik Col. 2,

line 67, "100" should be Col. 4, line 29, "29 should be --28-; C01. 6,line 51, "locations" should be --location; Col. 8, line 1, "with" shouldbe -within-; Col. 8, line 25,

after "20" insert --to-.

Signed and sealed this 4th day of April 1972.

(SEAL) Attest:

EDWARD M.FLETCHER,JR. ROBERT GOTTSCHALK Attesting Officer Commissionerof Patents

2. A method according to claim 1 further comprising: sequentiallyexciting the formation at a plurality of separate frequencies, measuringthe magnitude of the relatively large electRokinetic potentials at thecontact area and the magnitude of the proportionally smallerelectrokinetic potentials at at least one other location spaced from thecontact area by a distance large relative to the electrokinetic skindepth of the formation at each separate frequency of excitation, anddetermining the ratio of the magnitude of the electrokinetic potentialsat each other location to the magnitude of the electrokinetic potentialsat the contact area at each separate frequency.
 3. A method according toclaim 2 in which the frequencies at which the formation is excited arewithin the range of from 20 to 500 c.p.s.
 4. A method for investigatingthe permeability of earth formations traversed by a bore hole andcontaining a fluid in the pores thereof comprising: positioning a sonictransducer in contact with the surface of the bore hole within aformation to be investigated, actuating the transducer to periodicallyexcite the formation at the area of contact between the transducer andthe formation so as to cause periodic electrokinetic potentials ofrelatively large magnitude to be produced at the contact area andseparate, periodic electrokinetic potentials of proportionally smallermagnitude to be produced at locations spaced from the contact area,simultaneously with excitation of the formation measuring the magnitudeof the relatively large electrokinetic potentials at the contact areaand the magnitude of the proportionally smaller electrokineticpotentials at at least one other location spaced from the contact areaby a distance large relative to the electrokinetic skin depth of theformation, and determining the ratio of the magnitude of theelectrokinetic potentials at each other location to the magnitude of theelectrokinetic potentials at the contact area, said ratio being anindication of the permeability of the formation.
 5. A method accordingto claim 4 further comprising: sequentially exciting the formation at aplurality of separate frequencies, measuring the magnitude of therelatively large electrokinetic potentials at the contact area and themagnitude of the proportionally smaller electrokinetic potentials at atleast one other location spaced from the contact area by a distancelarge relative to the electrokinetic skin depth of the formation at eachseparate frequency of excitation, and determining the ratio of themagnitude of the electrokinetic potentials at each other location to themagnitude of the electrokinetic potentials at the contact area at eachseparate frequency.
 6. A method according to claim 5 in which thefrequency at which the formation is excited is within the range of from20 to 500 c.p.s.
 7. Apparatus for investigating the permeability ofearth formations traversed by a bore hole and containing a fluid in thepores thereof comprising: a source of periodic mechanical excitation,means for positioning the excitation source in contact with the borehole wall within a formation to be investigated, means for actuating thesource to periodically excite the formation at the area of contactbetween the source and the bore hole wall so as to cause periodicelectrokinetic potentials of relatively large magnitude to be producedat the contact area and separate, periodic electrokinetic potentials ofa proportionally smaller magnitude to be produced at locations spacedfrom the contact area, means for measuring the magnitude of therelatively large electrokinetic potentials at the contact area and themagnitude of the proportionally smaller electrokinetic potentials at atleast one other location spaced from the contact area by a distancelarge relative to the electrokinetic skin depth of the formation duringexcitation of the formation, and means for determining the ratio of themagnitude of the proportionally smaller electrokinetic potentials ateach other location to the magnitude of the relatively largeelectrokinetic potentials at the contact area, said ratio being anindication of the permeability of the formation.
 8. Apparatus accordingto claim 7 in which the source of periodic mechanical excitationcomprises a sonic transducer.
 9. Apparatus according to claim 8, inwhich the sonic transducer is adapted to produce excitation frequencieswithin the range of from 20 to 500 c.p.s.